1155 Heap Paths (30 分)

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (1<N≤1,000), the number of keys in the tree. Then the next line contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.

Output Specification:

For each given tree, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally print in a line Max Heap if it is a max heap, or Min Heap for a min heap, or Not Heap if it is not a heap at all.

Sample Input 1:

8
98 72 86 60 65 12 23 50

 

Sample Output 1:

98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap

 

Sample Input 2:

8
8 38 25 58 52 82 70 60

 

Sample Output 2:

8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap

 

Sample Input 3:

8
10 28 15 12 34 9 8 56

 

Sample Output 3:

10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap



AC代码：

#include<bits/stdc++.h>
using namespace std;
const int maxn=10010;
#define inf 0x3fffffff
int n;
int heap[maxn];
vector<int> v;
bool maxH(){
    for(int i=1;i<=n;i++){
        if(i*2>n){
            break;
        }
        if(heap[i*2]>heap[i]){
            return false;
        }
        if(i*2+1>n){
            break;
        }
        if(heap[i*2+1]>heap[i]){
            return false;
        }
    }
    return true;
}
bool minH(){
    for(int i=1;i<=n;i++){
        if(i*2>n){
            break;
        }
        if(heap[i*2]<heap[i]){
            return false;
        }
        if(i*2+1>n){
            break;
        }
        if(heap[i*2+1]<heap[i]){
            return false;
        }
    }
    return true;
}
vector<int> path,tempath;
void dfs(int u){
    if(u*2>n){
        v.push_back(heap[u]);
        for(auto it=v.begin();it!=v.end();it++){
            printf("%d",*it);
            if(it!=v.end()-1){
                printf(" ");
            }
        }
        printf("\n");
        v.pop_back();
        return ;
    }
    v.push_back(heap[u]);
    if(u*2+1<=n){
        dfs(u*2+1);
    }
    if(u*2<=n){
        dfs(u*2);
    }
    v.pop_back();
}
int main(){
    scanf("%d",&n);
    heap[0]=0;
    for(int i=1;i<=n;i++){
        scanf("%d",&heap[i]);
    }
    dfs(1);
    if(maxH()){
        printf("Max Heap\n");
    }
    else if(minH()){
        printf("Min Heap\n");
    }
    else{
        printf("Not Heap\n");
    }
    return 0;
}